MIT 18.03 Differential Equations, Spring 2006
Topics Ordinary Differential Equations, ODE, modeling physical systems, first-order ODE's, Linear ODE's, second order ODE's, second order ODE's with constant coefficients, Undetermined coefficients, variation of parameters, Sinusoidal signals, exponential signals, oscillations, damping, resonance, Complex numbers and exponentials, Fourier series, periodic solutions, Delta functions, convolution, Laplace transform methods Matrix systems, first order linear systems, eigenvalues and eigenvectors, Non-linear autonomous systems, critical point analysis, phase plane diagrams
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.
Producer MIT OpenCourseWareAudio/Visual sound, colorLanguage English
May 28, 2015
Missing Lecture 18?
Was there a test on this day, that the video was not recorded? If not, can it be uploaded?
Nevertheless, infinite THANKS! for uploading this!
April 2, 2012
A Word of Thanks!
I found the video lectures extremely useful in understanding about differential equations. These videos helps me improving my DE skills to a much higher level, studied along with rest of the material in MIT OCW. Great thing!!!